OFFSET
1,2
COMMENTS
A canonical finite permutation on positive integers is a bijective mapping of [n] = {1, ..., n} to itself, counting the empty mapping as a permutation of the empty set.
From Rémy Sigrist, Sep 18 2021: (Begin)
As usual with lists, the terms of the sequence are given in ascending order.
This sequence has connections with A175061; here the prime factorizations, there the run-lengths in binary expansions, encode finite permutations.
There are m! terms with m distinct prime factors, the least one being A006939(m) and the greatest one being A076954(m); these m! terms are not necessarily contiguous.
(End)
REFERENCES
Suggested by Franklin T. Adams-Watters
LINKS
EXAMPLE
Writing (prime(i))^j as i:j, we have this table:
Primal Codes of Canonical Finite Permutations
` ` ` 1 = { }
` ` ` 2 = 1:1
` ` `12 = 1:2 2:1
` ` `18 = 1:1 2:2
` ` 360 = 1:3 2:2 3:1
` ` 540 = 1:2 2:3 3:1
` ` 600 = 1:3 2:1 3:2
` `1350 = 1:1 2:3 3:2
` `1500 = 1:2 2:1 3:3
` `2250 = 1:1 2:2 3:3
` 75600 = 1:4 2:3 3:2 4:1
`105840 = 1:4 2:3 3:1 4:2
`113400 = 1:3 2:4 3:2 4:1
`126000 = 1:4 2:2 3:3 4:1
`158760 = 1:3 2:4 3:1 4:2
`246960 = 1:4 2:2 3:1 4:3
`283500 = 1:2 2:4 3:3 4:1
`294000 = 1:4 2:1 3:3 4:2
`315000 = 1:3 2:2 3:4 4:1
`411600 = 1:4 2:1 3:2 4:3
`472500 = 1:2 2:3 3:4 4:1
`555660 = 1:2 2:4 3:1 4:3
`735000 = 1:3 2:1 3:4 4:2
`864360 = 1:3 2:2 3:1 4:4
`992250 = 1:1 2:4 3:3 4:2
1296540 = 1:2 2:3 3:1 4:4
1389150 = 1:1 2:4 3:2 4:3
1440600 = 1:3 2:1 3:2 4:4
1653750 = 1:1 2:3 3:4 4:2
2572500 = 1:2 2:1 3:4 4:3
3241350 = 1:1 2:3 3:2 4:4
3601500 = 1:2 2:1 3:3 4:4
3858750 = 1:1 2:2 3:4 4:3
5402250 = 1:1 2:2 3:3 4:4
PROG
(PARI) See Links section.
(PARI) is(n) = { my (f=factor(n), p=f[, 1]~, e=f[, 2]~); Set(e)==[1..#e] && (#p==0 || p[#p]==prime(#p)) } \\ Rémy Sigrist, Sep 18 2021
CROSSREFS
KEYWORD
nonn
AUTHOR
Jon Awbrey, Jul 09 2005
EXTENSIONS
Offset changed to 1 and data corrected by Rémy Sigrist, Sep 18 2021
STATUS
approved